Let q=(3+i)/(1+i). Give all arguments as principal arguments in radians. - Express q in the form a+i

Question

Let q=(3+i)/(1+i). Give all arguments as principal arguments in radians. - Express q in the form a+ib, where a and b are exact real numbers. - By considering the numerator and denominator separately, find |q| and arg q. - Hence show that sin(pi)/(12)=(6- 2)/(4).

Accepted Answer

(a) $q=\frac{\sqrt3+1}{2}+\frac{1-\sqrt3}{2}i$ (b) $|q|=\sqrt2,\ \arg q=-\frac{\pi}{12}$ (c) $\sin\frac{\pi}{12}=\frac{\sqrt6-\sqrt2}{4}$

A quotient giving an exact sine value

A quotient giving an exact sine value

Solution:

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